Multiple Heckman Selection Model

TL;DR

This paper extends the Heckman selection model to matrix-valued data using a matrix normal distribution, enabling modeling of dependencies and selection bias with an efficient ECM algorithm.

Contribution

It introduces a novel matrix-variate Heckman model, develops an ECM algorithm with closed-form updates, and explores theoretical properties linking to the SUN distribution.

Findings

The model effectively captures dependencies across rows and columns.

Simulation studies demonstrate the model's accuracy and robustness.

Application to real datasets shows practical utility.

Abstract

We introduce a novel matrix-variate extension of the Heckman selection model to accommodate multiple outcomes, providing a flexible and natural generalization of classical selection models for matrix-valued data. By relying on the matrix normal distribution, the proposed model captures dependencies across both rows and columns while accounting for selection bias. An Expectation/Conditional Maximization (ECM) algorithm is developed, yielding closed-form updates for all model parameters. We investigate key theoretical properties, including the connection between sample selection models and the recently developed multivariate unified skew-normal (SUN) distribution. The performance of the proposed approach is assessed through simulation studies, and its practical utility is illustrated using two real datasets. The proposed method is implemented in the R package mvHeckman.